AnswersFL-1200310-Algebra 1 AIntroduction to Compound Inequalities

Introduction to Compound Inequalities — Unit test Answers

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Which number line represents the solutions to –2|x| = –6?

A
A number line from negative 8 to 8 in increments of 1. Two points, one at negative 6 and one at negative 2.
Option A
B
A number line from negative 8 to 8 in increments of 1. Two points, one at negative 8 and one at negative 4.
Option B
C
A number line from negative 8 to 8 in increments of 1. Two points, one at negative 4 and one at 4.
Option C
D
A number line from negative 8 to 8 in increments of 1. Two points, one at negative 3 and one at 3.
Option D
2
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In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105, which inequality represents p, the scores for students who are eligible for tutoring or extension activities?

A
85 < p < 125
B
85 ≤ p ≤ 125
C
p 125
D
p ≤ 85 or p ≥ 125
3

What is the value of x in the equation ?

Question illustration
A
StartFraction 2 Over 3 EndFraction left-parenthesis StartFraction one-half EndFraction. x plus 12 right-parenthesis equals left-parenthesis StartFraction one-half EndFraction left-parenthesis StartFraction one-third EndFraction x plus 14 right-parenthesis minus 3.
Option A
B
StartFraction one-half EndFraction left-parenthesis n minus 4 right-parenthesis minus 3 equals 3 minus left-parenthesis 2 n plus 3 right-parenthesis.
Option B
C
2
D
13
4

Deepak wrote out the steps to his solution of the equation – 3x – 5 + 4x = –. Which step has an incorrect instruction?

Question illustration
A
Step 1
B
Step 2
C
Step 3
D
Step 4
5

The inequality graphed below represents the ages, a, of players on a baseball team.

Question illustration
A
12 < a ≤ 18
B
12 ≤ a < 18
C
12 > a ≤ 18
D
12 ≥ a < 18
6

The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x – 72.5| = 4. What are the minimum and maximum temperatures in the house?

A
72.5°F and 76.5°F
B
68.5°F and 76.5°F
C
70.5°F and 74.5°F
D
72.5°F and 74.5°F
7

Which input value produces the same output value for the two functions on the graph?

Question illustration
A
x = –3
B
x = –1
C
x = 1
D
x = 3
8

Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x = 3x + 15 – 113x – 4 = 3x + 4

A
The equation has one solution: x = 0.
B
The equation has one solution: x = 8.
C
The equation has no solution.
D
The equation has infinite solutions.
9

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b.

A
h = (– b)÷ r
Option A
B
h = – b ÷ r
Option B
C
h = ÷ r – b
Option C
D
h = ÷ r
Option D
10

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse.

A
y = a · πx
B
y = a + (πx)
C
y = a – πx
D
y = a ÷ (πx)
11

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

A
–12 – 20x ≤ –6x + 9
B
–12 – 20x ≥ –6x + 9
C
–12 + 20x ≤ –6x + 9
D
–12 + 20x ≥ –6x + 9
12

Step 1: –10 + 8x < 6x – 4Step 2: –10 < –2x – 4Step 3: –6 < –2xStep 4: ________

A
x < –3
B
x > –3
C
x < 3
D
x > 3
13

Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?

A
He is correct because both solutions satisfy the equation.
B
He is not correct because he made a sign error.
C
He is not correct because there are no solutions.
D
He is not correct because there is only one solution: x = 5.
14

In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours or after working more than 9 hours. How can this be written as a single compound inequality?

A
7 < h < 9
B
7 > h > 9
C
h 9
D
h > 7 or h < 9
15

Fiona solved the equation shown. – (6x – 3) = –

Question illustration
A
Simplify by combining like terms.
B
Simplify by using addition property of equality.
C
Simplify by using the multiplication property of equality.
D
Simplify by using the division property of equality.
16

What value of x is in the solution set of 2x – 3 > 11 – 5x?

A
–3
B
0
C
2
D
4
17

Which situation could be represented by the graph?

Question illustration
A
Students in the children’s choir are at least 8 years old but no more than 11 years old.
B
Babysitters earn between $8 and $11 per hour.
C
A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.
D
The dogs at a veterinary clinic are all 8 years old or under or are older than 11 years.
18

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

A
|x – 3| = 45; minimum angle: 42 degrees
B
|x – 3| = 45; minimum angle: 45 degrees
C
|x – 45| = 3; minimum angle: 42 degrees
D
|x – 45| = 3; minimum angle: 45 degrees
19

What is the value of n in the equation ?

Question illustration
A
n = 0
B
n = 2
C
n = 4
D
n = 6
20

The formula to convert °F to °C is C = (F – 32).Convert 50°C to °F.

Question illustration
A
10°F
B
20°F
C
122°F
D
132°F

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